Bound states in the 3d Ising model and implications for QCD at finite temperature and density

TL;DR

This paper investigates the bound state spectrum of the 3D Ising model near criticality and explores its implications for understanding phase transitions in hot QCD at finite density, proposing a correspondence between Ising bound states and QCD diquarks.

Contribution

It identifies an unbinding line in the 3D Ising model and conjectures its equivalence to a phase boundary in hot QCD, linking bound states to diquarks.

Findings

Existence of an unbinding line in the Ising model near criticality.

Numerical evidence suggests the unbinding line coincides with the critical beta axis.

Conjecture that the unbinding line corresponds to the phase boundary in QCD.

Abstract

We study the spectrum of bound states of the three dimensional Ising model in the (h,beta) plane near the critical point. We show the existence of an unbinding line, defined as the boundary of the region where bound states exist. Numerical evidence suggests that this line coincides with the beta=beta_c axis. When the 3D Ising model is considered as an effective description of hot QCD at finite density, we conjecture the correspondence between the unbinding line and the line that separates the quark-gluon plasma phase from the superconducting phase. The bound states of the Ising model are conjectured to correspond to the diquarks of the latter phase of QCD.